A stepped balloon catheter prosthesis deployment system is disclosed for placement of a prosthesis across an Os opening from a main body lumen to a branch body lumen. The prosthesis comprises a radially expansible support at one end, a circumferentially extending link at the other end and at least one frond extending axially therebetween. The prosthesis is configured to be deployed from a stepped diameter balloon with the support in the branch body lumen, with the circumferentially extending link in the main lumen and the frond extendable across the Os.